The transmission device must make it possible to take up the manufacturing tolerances of the seat back, of the seat proper, and of the locking device of the runner that connects the seat proper to the floor of the vehicle.
Such a transmission device is known, in particular, from French Patent Application FR 2 800 021. That transmission device comprises, in particular, a spring that has a first end connected to the locking device of the runner and a second end connected to a sleeve which is itself secured to a cable connected to the back of the seat. However, with that type of transmission device, the traction spring is designed to be stretched throughout the pivoting of the seat back so as to absorb the stroke or pivoting of the seat back after the locking device of the runner has been unlocked. That known transmission device thus requires a relatively large space to be provided in order to enable the spring to stretch throughout the pivoting of the seat back, in spite of small amount of internal space available in vehicle seats.